Patent document 1 discloses a technique as a valve opening and closing timing control apparatus including the aforementioned construction, the valve opening and closing timing control apparatus including a hypo-cycloid deceleration mechanism where a ring gear is fixed to an inner peripheral wall of a driving-side rotational member (a sprocket in Patent document 1), and an inner gear (a planetary gear in Patent document 1) is supported at an eccentric shaft eccentric to a center axis of the driving-side rotational member, a part of teeth provided at the inner gear being meshed with a part of teeth provided at an inner periphery of the ring gear. Patent document 1 discloses a construction including an electric actuator (an electromagnetic portion in Patent document 1) and a driven-side rotational member (an output shaft in Patent document 1) which is connected to a camshaft and at which plural engagement bores are formed, the plural engagement bores engaging with engagement projections of the inner gear.
According to the aforementioned construction, the inner gear rotates by driving of the electric actuator relative to the ring gear by an angle corresponding to a difference between the number of teeth of the ring gear and the number of teeth of the inner gear based on revolution of the inner gear which is supported at the eccentric shaft. Because the engagement projections of the inner gear engage with the engagement bores of the driven-side rotational member, the driven-side rotational member rotates by an angle corresponding to a rotation angle of the inner gear relative to the driven-side rotational member as a result of driving of the electric actuator.